beatfrequency

Beat frequency is the rate at which the amplitude of the superposition of two waves fluctuates due to their close frequencies. When two sinusoidal waves with frequencies f1 and f2 and similar amplitudes are added, the result can be expressed as a carrier at the average frequency (f1 + f2)/2 whose amplitude is modulated at a rate equal to the absolute difference |f1 − f2|. The envelope oscillates with a period of 1/|f1 − f2|, so the beat frequency heard is |f1 − f2| Hz.

In acoustics, beats are heard as a periodic waxing and waning of loudness. The audible beat rate corresponds to the frequency difference, while the perceived pitch is near the average of the two frequencies. Beats are commonly observed when tuning musical instruments; a tuning fork or pitch reference is adjusted until the beat rate slows to zero, indicating matching frequencies. The human ear can typically perceive beats up to about 15–20 Hz; larger differences produce rapid fluctuations that blend into a rough sound rather than discrete beats.

Beyond acoustics, beat phenomena occur in any wave system. In radio engineering, heterodyne reception uses a local oscillator to mix with an incoming signal, producing an intermediate frequency equal to the difference between the two frequencies. In optics, two nearly identical laser frequencies produce an optical beat that can be detected with a photodetector, useful in interferometry and frequency metrology.

Beat frequency, therefore, is a general descriptor of the frequency of amplitude modulation arising from the interference of two waves with nearby frequencies.